Vague Regions

In many geographical applications there is a need to model spatial phenomena not simply by sharp objects but rather through indeterminate or vague concepts. To support such applications we present a model of vague regions which covers and extends previous approaches. The formal framework is based on a general exact model of spatial data types. On the one hand, this simplifies the definition of the vague model since we can build upon already existing theory of spatial data types. On the other hand, this approach facilitates the migration from exact to vague models. Moreover, exact spatial data types are subsumed as a special case of the presented vague concepts. We present examples and show how they are represented within our framework. We give a formal definition of basic operations and predicates which particularly allow a more fine-grained investigation of spatial situations than in the pure exact case. We also demonstrate the integration of the presented concepts into an SQL-like query language.

[1]  Ralf Hartmut Güting,et al.  Explicit Graphs in a Functional Model for Spatial Databases , 1994, IEEE Trans. Knowl. Data Eng..

[2]  Alexandroff.,et al.  Elementary concepts in Topology , 1932 .

[3]  Reza Banai,et al.  Fuzziness in Geographical Information Systems: Contributions from the Analytic Hierarchy Process , 1993, Int. J. Geogr. Inf. Sci..

[4]  John T. Finn,et al.  Use of the Average Mutual Information Index in Evaluating Classification Error and Consistency , 1993, Int. J. Geogr. Inf. Sci..

[5]  Agnès Voisard,et al.  Thematic Map Modeling , 1989, SSD.

[6]  P. S. Aleksandrov,et al.  Elementary concepts of topology , 1961 .

[7]  Martin Erwig,et al.  Graphs in Spatial Databases , 1994, GI Datenbank Rundbrief.

[8]  David Altman,et al.  Fuzzy Set Theoretic Approaches for Handling Imprecision in Spatial Analysis , 1994, Int. J. Geogr. Inf. Sci..

[9]  Markus Schneider,et al.  Spatial Data Types for Database Systems , 1997, Lecture Notes in Computer Science.

[10]  Anthony G. Cohn,et al.  The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries , 2020 .

[11]  S. Lane,et al.  Point set topology , 1964 .

[12]  Ralf Hartmut Güting,et al.  Geo-Relational Algebra: A Model and Query Language for Geometric Database Systems , 1988, EDBT.

[13]  Ralf Hartmut Güting,et al.  Realms: A Foundation for Spatial Data Types in Database Systems , 1993, SSD.

[14]  Robert B. Tilove,et al.  Set Membership Classification: A Unified Approach to Geometric Intersection Problems , 1980, IEEE Transactions on Computers.

[15]  Philippe Lagacherie,et al.  Fuzziness and Uncertainty of Soil Boundaries: From Reality to Coding in GIS , 2020 .

[16]  Michael F. Worboys,et al.  A Canonical Model for a Class of Areal Spatial Objects , 1993, SSD.

[17]  Vassiliki J. Kollias,et al.  Fuzzy reasoning in the development of geographical information systems FRSIS: a prototype soil information system with fuzzy retrieval capabilities , 1991, Int. J. Geogr. Inf. Sci..

[18]  Fangju Wang,et al.  Fuzzy Representation of Geographical Boundaries in GIS , 1996, Int. J. Geogr. Inf. Sci..

[19]  Michael Blakemore,et al.  Part 4: Mathematical, Algorithmic and Data Structure Issues: Generalisation and Error in Spatial Data Bases , 1984 .

[20]  SchneiderMarkus,et al.  Realm-based spatial data types , 1995, VLDB 1995.

[21]  Fangju Wang Towards a Natural Language User Interface: An Approach of Fuzzy Query , 1994, Int. J. Geogr. Inf. Sci..

[22]  E. J.,et al.  Topological relations between regions with holes * , 1994 .

[23]  Karl Neumann,et al.  Modelling and Manipulating Objects in Geoscientific Databases , 1986, ER.

[24]  Fangju Wang,et al.  Fuzzy information representation and processing in conventional GIS software: database design and application , 1990, Int. J. Geogr. Inf. Sci..